Starry Night of the Final Day by Tavoriel
did y’all know?
that in the box topology, R^[omega], a countably infinite Cartesian product of the reals with the reals with the reals…, isn’t connected?!
This is among the reasons why we prefer the product topology, in which open sets in X x X x X x… are products of finitely many open sets in the various X’s and the rest the complete sets, as opposed to the box topology where open sets are merely products of open sets in the spaces composing the product.
MATH IS SO COOL. AND SO WEIRD.
